# Method for estimating T2

A method for providing an estimated 3D T2 map for magnetic resonance imaging using a Double-Echo Steady-State (DESS) sequence for a volume of an object in a magnetic resonance imaging (MRI) system is provided. A DESS scan of the volume is provided by the MRI system. Signals S1 and S2 are acquired by the MRI system. Signals S1 and S2 are used to provide a T2 map for a plurality of slices of the volume, comprising determining repetition time (TR), echo time (TE), flip angle α, and an estimate of the longitudinal relaxation time (T1), and wherein the DESS scan has a spoiler gradient with an amplitude G and a duration τ and ignoring echo pathways having spent more than two repetition times in the transverse plane.

## Latest The Board of Trustees of the Leland Stanford Junior University Patents:

**Description**

**CROSS REFERENCE TO RELATED APPLICATIONS**

This application claims priority under 35 U.S.C. § 119(e) from U.S. Provisional Application No. 62/324,328, entitled “SIMPLE ESTIMATION OF T2 MAPS USING THE DOUBLE-ECHO STEADY-STATE SEQUENCE”, filed Apr. 18, 2016.

**GOVERNMENT RIGHTS**

This invention was made with Government support under contracts AR063643 and EB002524 and P41EB015891 awarded by the National Institutes of Health. The Government has certain rights in the invention.

**BACKGROUND OF THE INVENTION**

This invention relates generally to magnetic resonance imaging (MRI). Magnetic resonance imaging (MRI) is a non-destructive method for the analysis of materials and is an approach to medical imaging. It is generally non-invasive and does not involve ionizing radiation. In very general terms, nuclear magnetic moments are excited at specific spin precession frequencies which are proportional to the local magnetic field. The radio-frequency signals resulting from the precession of these spins are received using pickup coils. By manipulating the magnetic fields, an array of signals is provided representing different regions of the volume. These are combined to produce a volumetric image of the nuclear spin density of the body.

Magnetic resonance (MR) imaging is based on nuclear spins, which can be viewed as vectors in a three-dimensional space. During MRI, each nuclear spin responds to four different effects: precession about the main magnetic field, nutation about an axis perpendicular to the main field, and both transverse and longitudinal relaxation.

**SUMMARY OF THE INVENTION**

In accordance with the invention, a method for providing an estimated 3D T_{2 }map for magnetic resonance imaging using a Double-Echo Steady-State (DESS) sequence for a volume of an object in a magnetic resonance imaging (MRI) system is provided. A DESS scan of the volume is provided by the MRI system. Signals S_{1 }and S_{2 }are acquired by the MRI system. Signals S_{1 }and S_{2 }are used to provide a T_{2 }map for a plurality of slices of the volume, comprising determining repetition time (TR), echo time (TE), flip angle α, and an estimate of the longitudinal relaxation time (T_{1}), and wherein the DESS scan has a spoiler gradient with an amplitude G and a duration τ and ignoring echo pathways having spent more than two repetition times in the transverse plane.

In another manifestation, a method for providing an estimated 3D T_{2 }map for magnetic resonance imaging using a Double-Echo Steady-State (DESS) sequence for a volume of an object in a magnetic resonance imaging (MRI) system is provided. A DESS scan of the volume is provided by the MRI system. Signals S_{1 }and S_{2 }are acquired by the MRI system. S_{1 }and S_{2 }are used to provide a T_{2 }map for a plurality of slices of the volume, using the equation

wherein ƒ(α, TR, T1) is a function that is not proportional to

and TR is a repetition time, TE is an echo time, and α is a flip angle.

The invention and objects and features thereof will be more readily apparent from the following detailed description and appended claims when taken with the drawings.

**BRIEF DESCRIPTION OF THE DRAWINGS**

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

_{2 }estimates from a DESS scan.

_{2 }estimate to errors in the T_{1 }and a assumptions.

**DETAILED DESCRIPTION OF ILLUSTRATED EMBODIMENTS**

1. Introduction

The Double-Echo Steady-State (DESS) sequence offers distortion-free, SNR-efficient 3D-imaging with good contrast flexibility. DESS is a gradient-spoiled steady-state sequence, collecting two echoes per repetition (TR), with the spoiler gradient separating the two echoes. The two signals, often labeled S_{1 }(before the spoiler) and S_{2 }(after the spoiler), have different contrast. The S_{1 }signal is often said to have T_{1}/T_{2 }weighting and S_{2 }to have a mixture of T_{2 }and diffusion weighting, but in reality both the contrasts are quite complicated functions of the extrinsic scan parameters (TR, TE, flip angle α, gradient amplitude G and gradient duration τ) as well as the intrinsic tissue parameters (T_{1}, T_{2}, and diffusivity). While DESS has been used for various anatomies, such as the breast and the prostate, it has found particularly widespread use for musculoskeletal imaging, where, for example, it has been used in the Osteoarthritis Initiative (OAI) to determine Osteoarthritis (OA) progression.

To improve OA detection, DESS has been used for quantitative imaging of T_{2 }and apparent diffusion coefficient (ADC). These have been found to correlate with collagen network organization and proteoglycan concentration, respectively. A number of signal models have been developed to quantitatively describe both of the DESS signals and their dependency on tissue parameters. These include both closed-form and non-closed-form analytical methods as well as numerical methods.

Some methods model the DESS signals completely and can be considered fully accurate for a single T_{1}, T_{2}, and diffusivity in a voxel. However, owing to their complexity, using these models for parameter estimation typically requires solving them with a numerical search over a predetermined solution set. This inhibits immediate, automatic creation of parameter maps right at the scanner, which would be of great value for clinical scans. Furthermore, a method in Freed D E, Scheven U M, Zielinski L J, Sen P N, Hürlimann M D. Steady-state free precession experiments and exact treatment of diffusion in a uniform gradient. Journal of Chemical Physics. 2001; 115(9):4249-4258, which is incorporated by reference for all purposes, and which describes the magnetization with a continued fraction, does not allow for pulsed gradients. For these reasons, approximate models are often used to estimate the desired parameter in spite of known errors. For example, in Welsch G H, Scheffler K, Mamisch T C, Hughes T, Millington S, Deimling M, Trattnig S. Rapid Estimation of Cartilage T_{2 }Based on Double Echo at Steady State (DESS) With 3 Tesla. Magnetic Resonance in Medicine. 2009; 62:544-549, which is incorporated by reference for all purposes, the following model, originally suggested in Bruder H, Fischer H, Graumann R, Deimling M. A New Steady-State Imaging Sequence for Simultaneous Acquisition of Two MR Images with Clearly Different Contrasts. Magnetic Resonance in Medicine. 1988; 7:35-42, which is incorporated by reference for all purposes, was used to estimate T_{2 }from a single DESS scan:

This relationship essentially describes a spin echo relationship between S_{2 }and S_{1 }in consecutive TRs. Although this approach may offer useful results in spite of errors in T_{2}, practical T_{2 }mapping would benefit from a comparably simple analytical formula that is even more accurate.

An embodiment of the invention provides a model that can be used for T_{2 }estimation from a single DESS scan. Our analysis demonstrates that higher-order echo pathways can often be ignored, based on pathway cancellation effects and signal decay, leading to a simple and accurate linear relationship between the signals from two DESS echoes. We validate the overall approach using simulations, phantom scans, and in vivo knee scans.

2. Theory

2.1 Derivation of Simplified Signal Ratio

A simple yet accurate linear approximation of the relationship between the two DESS echoes can be derived by tracing the components that contribute to the magnetization, starting at S_{2}, until we arrive at S_{1}. We use the Extended Phase Graph (EPG) formalism, which decomposes magnetization into a basis of positively and negatively dephased transverse states (coefficients F_{0}, F_{1}, F_{2}, . . . ) as well as sinusoidally varying longitudinal states (coefficients Z_{0}, Z_{1}, Z_{2}, . . . ). The procedure is explained graphically in *a*-*c*_{n }and Z_{n}) that multiply transverse states with n cycles of positive or negative dephasing, and longitudinal states with n cycles of sinusoidal variation:

where an asterisk (*) denotes a complex conjugate. The observable signal is the DC transverse term F_{0}. Relaxation and diffusion over time are represented by scaling of the elements (T_{1 }relaxation is represented by an additive factor to the DC longitudinal term, Z_{0}) and the effect of a gradient is represented by shifting the transverse coefficients F_{n}.

The effects of T_{1}/T_{2 }decay, as well as diffusion, on state n, can be described by the scaling terms

(assuming the gradient in the center of the TR). The effect of an RF pulse with flip angle α and phase ϕ is represented by matrix multiplication with the matrix:

Here, TR and TE represent the repetition and echo time, respectively, α is the flip angle, D is the diffusivity, and the dephasing per unit length induced by the unbalanced gradient is denoted by Δk=γGτ, where G and τ are the spoiler amplitude and duration, respectively, and γ is the gyromagnetic ratio. We label the states immediately before/after the RF pulse with −/+ superscripts, respectively. To determine a relationship between the two DESS signals, we look at the echo pathway of the observable signal immediately before the pulse, F_{0}^{−}, and write down the components that contributed to it. We repeat this until we reach the observable signal immediately after the pulse, F_{0}^{+} (_{2 }signal in Buxton R B. The Diffusion Sensitivity of Fast Steady-State Free Precession Imaging. Magnetic Resonance in Medicine. 1993; 29:235-243, which is incorporated by reference for all purposes. We will assume ϕ=90°, resulting in real valued states, without loss of generality.

Combining Eqs. (4a-b) and using some algebra and trigonometric identities yields

Using the stated expressions for the decay factors as well as the fact that the observed signal magnitudes are

(where we have used that the two signals are out of phase and the second signal experiences T_{2}′ rephasing), we arrive at the following expression:

In each panel of *a*-*c***2**) before the RF pulse is the “negatively dephased” signal following the previous RF pulse. (b) Two relevant paths before the RF pulse contribute to the state in panel **1***a*, shown with black arrows. These are transverse and longitudinal states that have a net dephasing from one gradient. They also contribute to the longitudinal state following the RF pulse (gray arrows). (c) The measurable signal following the previous RF pulse (S**1**), before dephasing by the gradient, contributes to the “positively dephased” transverse pathway from *b***1** and S**2** that can be easily solved, resulting in Eq. (6).

This relationship, which assumes the echoes are acquired symmetrically during the TR (with the same duration from the RF pulse to S_{1 }as from S_{2 }to the subsequent RF pulse), provides a simple analytic estimate of T_{2 }given an estimate of T_{1 }and either minimal diffusion sensitivity or an estimate of diffusivity.

In the case of low spoiling (Δk≈0), the model reduces to the following relationship:

For α=90°, this further reduces to

In the case of very long T_{1}, Eq. (7) becomes independent of flip angle and results in Eq. (1). This equation was presented by Bruder et al. and has been used by Welsch et al, for T_{2 }estimation in cartilage. However, this relationship results in errors unless the flip angle is close to 90° or TR/T_{1 }is very small. The relationship also assumes weak spoiling so that diffusion effects may be ignored. Eq. (6) better approximates the signal over a large range of T_{1}, flip angle α, and (zeroth) spoiler gradient moments. This is demonstrated in *a*_{1 }value of 1.2 s for cartilage, assuming both weak and strong spoiling (with spoiler moments of 0.001 and 156.6 mT/m·ms, respectively), as well as a long T_{1 }value of 5 s for the weakly spoiled case, and a TR of 22.5 ms. Other parameters were TE=6.5 ms, T_{2}=40 ms, gradient duration τ=3.4 ms, and ADC=1.6·10^{−3 }mm/s. In order for Eq. (1) to be valid with smaller flip angles (about 20°-60°), T_{1 }clearly needs to be much larger than TR.

*a *_{2}=40 ms. The blue (bottom) curves correspond to strong spoiling (gradient moment 156.6 mT/m·ms) and the green (middle) curves to weak spoiling (gradient moment 0.001 mT/m·ms), both with T_{1}=1.2 s. The red (top) curves correspond to weak spoiling and T_{1}=5 s. The green curves represent DESS scans that can be used for T_{2 }estimation in cartilage.

2.2 Cancellation of Higher-Order Echo Pathways

The model in Eq. (6) performs well for two reasons. The equation neglects the contribution of echo pathways between S_{1 }and S_{2 }that have spent more than two TRs in the transverse plane. This is partly justified by simple signal decay—the more time that the magnetization spends in the transverse plane, the more it will be attenuated both by T_{2 }relaxation and diffusion. However, a more important mechanism is the cancellation of echo pathways due to opposing phase, independent of relaxation. It is easy to show that all contributions to S_{2 }that have experienced two transverse TRs will have negative phase relative to S_{1}. However, this does not hold for higher order echo pathways. For example, if we denote TRs where the magnetization starts in the +/−n^{th }transverse state or the n^{th }longitudinal state by F_{−/−n }and Z_{n}, then the pathways F_{0}F_{1}F_{−2}F_{−1 }and F_{0}Z_{1}F_{1}F_{−2}F_{−1 }will have opposite sign. By accumulating the contributions of all such pathways, the positive and negative contributions (relative to S_{1}) of higher-order pathways can be modeled and compared. For example, by including pathways with two and four transverse TRs, Eq. (6) can be extended to

where B_{2−} is the two-TR component given by Eq. (6), and B_{4+} and B_{4−} are the four-TR components with the same and opposite phase to S_{1}, respectively, given by

*b *_{n+} and B_{n−} for n=2-12 over a range of flip angles with the same parameters as the green curve in *a**b *_{2}/S_{1 }from pathways spending 2-12 TRs in the transverse plane. The black curves represent the sum of the different pathways. For pathways of order 6 and above, the positive (×) curves overlap with the negative (solid) curves. The higher-order components with positive and negative phase have very similar magnitude. Therefore, they will have a negligible effect on the final answer, particularly for flip angles above 20° or short T_{2}. This is demonstrated in *c*_{2}/S_{1 }very accurately, even in cases where there is very little T_{2 }decay, such as in fluid. *c **b **d **c*_{1}=3.6 s and T_{2}=0.77 s, showing that the proposed model (blue signal) approximates the true signal (black curve) well for flip angles above 20°, even for long T_{1 }and T_{2}. The higher-order pathways contribute more to the signal ratio in this case, especially for low flip angles, but Eq. (6) nonetheless approximates the true signal well for flip angles above 20°.

3. Methods

In an embodiment, all scans were performed on a 3T 750 scanner (GE Healthcare, Waukesha, Wis., USA). Informed consent was obtained from all subjects in accordance with the Institutional Review Board protocol at our institution. The volunteer scans used a 16-channel receive coil wrapped around the knee (GEM Flex by NeoCoil, Waukesha, Wis., USA), the phantom scans used a single-channel transmit-receive wrist coil (GE BC-10 by Mayo Clinic, Rochester Minn., USA), and the patient scans used an 8-channel transmit-receive knee coil (Knee Array Coil by Invivo, Gainesville, Fla., USA).

3.1 Phantom Scans

Three agar phantoms were scanned using DESS with scan parameters TR=13.4 ms, TE=3.9 ms, voxel size 0.47×0.47×3.0 mm^{3}, spoiler moment 7.83 mT/m·ms and duration τ=3.4 ms, and flip angles α=10°, 15°, 20°, 30°, 40°, and 50°. Fast spin-echo (FSE) scans with echo times TE=17, 26, 34, 43, 51, 60, and 68 ms, TR=1000 ms and voxel size 0.47×0.47×6.0 mm^{3 }were performed and fitted to a monoexponential curve to obtain a reference T_{2}. The T_{2 }value was estimated from the DESS scans using Eqs. (1) and (7) and compared to the value resulting from the reference FSE scans. For Eq. (7), reference T_{1 }values known to be T_{1-1}=2000 ms, T_{1-2}=1700 ms, and T_{1-3}=1600 ms, measured with a 3TI MP-RAGE technique, and a flip angle measured with the Bloch-Siegert method, were used for processing each phantom.

3.2 Volunteer Scans

To test Eq. (7) in vivo, a sagittal DESS scan was performed in the knee of three healthy volunteers. The scans used a spoiler with a moment of 15.66 mT/m·ms and duration 3.4 ms. Other parameters were α=25°, TR=22.5 ms, TE=6.5 ms, slice thickness 3.0 mm. A spectrally selective RF pulse was used. The T_{2 }of the cartilage was again estimated using the linear approximations of Eqs. (1) and (7). Reference FSE scans were acquired with TE=9, 18, 27, 36, 45, 54, 63, and 72 ms and TR=1000 ms. Both scans were run with FOV=13 cm×13 cm and acquisition matrix 384×384, which was automatically interpolated to 512×512 by the scanner. For T_{2 }quantification using Eq. (7), T_{1}=1.2 s, typical for cartilage at 3T, and the prescribed flip angle of α=25° were used. Eq. (7) has low sensitivity to T_{1}, so small errors in the T_{1 }assumption should not cause large errors in estimated T_{2}. Furthermore, T_{1 }in knee cartilage does not change much whereas T_{2 }is sensitive to degeneration. For comparison, a T_{2 }map using a full numerical fit was produced from the DESS scan as well. This involved computing a dictionary of signal ratios for T_{2 }ranging between 10-100 ms (with a step size of 1 ms) using large EPG matrices (with 6 states) and then choosing the dictionary entry that best fitted each pixel. The total scan time was 6:26 min for FSE (acquiring 6 slices) and 5:11 min for DESS (acquiring 36 slices). In slices where both scans displayed clear anterior and posterior regions of the femoral cartilage, the resulting T_{2 }maps in those two regions were divided into deep and superficial regions, resulting in 4 regions per slice. This was possible in 10 slices, resulting in a total of 40 regions. The root-mean-squared (RMS) difference between the results from Eq. (7) and the FSE results was computed and compared to the difference between the results from Eq. (1) and the reference scans. The T_{2 }maps were computed in Matlab (The MathWorks, Natick, Mass.) on a Linux terminal with 128 GB of RAM and 32 2.6 GHz CPUs.

3.3 Patient Scans

As an initial demonstration of the value of Eq. (7) for routine diagnostic imaging, we selected data from three patients from a larger group scanned with DESS in a clinical setting (spoiler moment=31.32 mT/m·ms, spoiler duration=3.4 ms, α=20°, TR=20.4 ms, TE=6.4 ms, FOV=16 cm×16 cm, acquisition matrix 416×512, 80 slices with thickness of 1.6 mm interpolated to 0.8 mm (160 slices), 2× parallel imaging in the phase encode direction, scan time=5:00). T_{2 }maps were constructed automatically at the scanner. A proton-density (PD) weighted scan was acquired for comparison.

4. Results

4.1 Phantom Scans

The results from the phantom scans are shown in _{2 }values were T_{2-1}=62 ms, T_{2-2}=44 ms, and T_{2-3}=31 ms for the three phantoms. Eq. (1) underestimates T_{2 }compared to the reference FSE estimate, and this becomes more pronounced for smaller flip angles. The results are shown from estimating T_{2 }from DESS using Eq. (1) (dashed) and Eq. (7) (solid) as well as from reference FSE scans (dotted). For all phantoms, Eq. (7) clearly agrees better with the reference value than Eq. (1), and for flip angles of 20° or higher, Eq. (7) agrees very well with the reference scans, but gives a substantial overestimate in the case of a large T_{2 }and 10° or 15° flip angles. However, the error is much smaller than the error from Eq. (1).

4.2 Volunteer Scans

*a*-*h *_{2 }estimates from the DESS scan, using Eqs. (1) and (7), as well as the results from the reference FSE scans and a full numerical fit. The maps from Eq. (7) are more visually similar to the reference scans than those of Eq. (1) (*a*-*c***4***f*). This demonstrates that Eq. (7) gave T_{2 }estimates that better agreed with FSE estimates than Eq. (1). The full numerical fit gives very similar results to those obtained by Eq. (7), as shown both by its T_{2 }map and by a difference map (scaled by 10), while taking around 60× longer to produce, with an average processing time of 577 s per DESS data set (36×512×512 data points) compared to 9 s for Eq. (7).

*a *_{1}) from a sample sagittal DESS scan. *b *_{2}) from the same DESS scan. The windowing level is not the same as in *a**c *_{2 }map from FSE scans of the subject in *a*-*b**d *_{2 }map of articular cartilage from the DESS scan in panels a-b using Eq. (1). *e *_{2 }map using Eq. (7). *f *_{2 }map using a full numerical fit. The map looks very similar to the one in *e**g **e *and *f**h *_{2 }estimates from 4 regions of femoral cartilage in a total of 10 slices from 3 subjects. The trend line for Eq. (7) (green) better agrees with the FSE scans.

4.3 Patient Scans

*a*-*d *_{2 }map shows a focal decrease in T_{2 }values. *a **b **a*-*b **c *_{2 }maps resulting from applying Eq. (7) to the data in *a*-*b**d *

In another patient (not shown), the availability of the DESS T_{2 }map made it possible to visualize an oblique meniscal tear in the anterior horn of the medial meniscus, which was challenging to delineate with only the morphological images. In a third patient (not shown), a T_{2 }map acquired with DESS indicated tendinopathy where the patellar tendon had increased T_{2 }values at its insertion site, which was also relatively challenging to visualize with only the morphological DESS images.

5. Discussion

The DESS sequence allows 3D estimation of T_{2 }in cartilage with high SNR efficiency. The signal expressions are complicated, often necessitating imprecise simplifications or time-consuming numerical modeling of the signals. This study explores a linear relationship between the two DESS signals that can be used for accurately estimating T_{2 }from a single scan. Some embodiments have focused on applying the method in cartilage. Other embodiments could be used in various other anatomies. This could include T_{2 }mapping in breast cancer patients, which has been impractical due to the time consuming nature of spin-echo-based T_{2 }measurements.

The scan time for DESS used in this study was about 5 minutes. The patient scans were acquired at a higher resolution than the volunteer scans, but using parallel imaging, the scan time remained at 5 minutes at a cost in SNR. Scan time could be reduced by using lower resolution, higher readout bandwidth, fewer slices, or shorter RF pulses. However, in our experience, a 5 minute scan time is acceptable, especially considering that these 3D scans provide both morphological and quantitative information. Potentially, DESS could replace sagittal FSE scans that are widely used in many current protocols, but this needs to be studied further.

As mentioned, using the linear approximation of Eq. (7) for estimating T_{2 }from a single DESS scan requires an assumed T_{1 }value. This should not lead to large estimation errors, since the method has little sensitivity to T_{1}, which is also not expected to change much in cartilage. For example, using the same scan parameters as for the middle curve in *a*_{1}=1.2 s, yields T_{2 }estimates of 38.8 ms and 41.8 ms (−3.0% and +4.5%) when the real T_{1 }is 0.96 s and 1.44 s (i.e., the actual T_{1 }is 20% lower or higher than the assumed value), respectively. Both values are relatively close to the actual value of 40.0 ms. A correct assumption of T_{1}=1.2 s yields T_{2}=40.6 ms (+1.5%), a slight overestimate due to the approximation made. Similarly, sensitivity to B_{1 }results in estimates of 36.9 ms and 43.1 ms (−7.75% and +7.75%) when the actual flip angle α is 20° and 30° (i.e., 20% lower or higher than the assumed value of 25°). The B_{1 }sensitivity could be mitigated by acquiring a B_{1 }map along with the DESS scan. The sensitivity of the T_{2 }estimate to errors in the T_{1 }and a assumptions is further demonstrated in _{1 }and flip angle will always be needed when estimating T_{2 }from a single DESS scan, regardless of the model used. _{2 }estimation method in Eq. (7) to errors in the assumption of T_{1 }and B_{1}. The true T_{2 }is 40 ms. The flip angle α and T_{1 }are assumed to be 25° and 1.2 s, but actually vary from these values by +/−20%. Other scan parameters were the same as in *a*_{1 }are correct.

An embodiment can also be used in combination with other methods for quantitative DESS imaging. An embodiment could estimate other parameters such as T_{1 }or flip angle. Another embodiment would drive from Eq. (6):

This relationship is independent of T_{2}, and largely insensitive to T_{1}.

In conclusion, an embodiment provides a simplified expression for the ratio between the DESS signals, providing good T_{2 }estimation. The expression disregards higher-order echo pathways, an assumption we have shown to be valid due to both decay and cancellation of such pathways. The expression takes into account signal dependency to T_{1 }and flip angle, and we have shown that the method works well by assuming a T_{1 }typical for the tissue and using the prescribed flip angle in calculations.

6. Algorithm

To facilitate understanding, **704**). Signals S_{1 }and S_{2 }are acquired by the MRI system from the volume (step **708**). Signals S_{1 }and S_{2 }are used to provide a T_{2 }map for a plurality of slices of the volume, comprising determining repetition time (TR), echo time (TE), flip angle α, and an estimate of the longitudinal relaxation time (T_{1}), and wherein the DESS scan has a spoiler gradient with an amplitude G and a duration τ and ignoring echo pathways having spent more than two repetition times in the transverse plane (step **712**). If the diffusivity of the tissue D is known, then Eq. (6) can be used along with the spoiler gradient amplitude G and duration τ. A T_{2 }map is displayed (step **716**).

In one example, Eq. (7) may be used to provide the T_{2 }map from signals S_{1 }and S_{2 }with known values of TR, TE, α, and longitudinal relaxation time (T_{1}). The use of Eq. (7) allows echo pathways that have spent more than two repetition times in the transverse plane to be ignored. In addition, the use of Eq. (7) allows the T_{2 }map to be generated, while ignoring diffusivity, and estimating T_{1}. In another example, diffusivity is measured and Eq. (6) is used to provide the T2 map from signals S_{1 }and S_{2 }with known values of TR, TE, α, and an estimate of T_{1}.

**800** that may be used in an embodiment of the invention. The MRI system **800** comprises a magnet system **804**, a patient transport table **808** connected to the magnet system, and a controller **812** controllably connected to the magnet system. In one example, a patient would lie on the patient transport table **808** and the magnet system **804** would pass around the patient. The controller **812** would control magnetic fields and radio frequency (RF) signals provided by the magnet system **804** and would receive signals from detectors in the magnet system **804**.

**900**, which may be used to provide the controller **812**. The computer system may have many physical forms ranging from an integrated circuit, a printed circuit board, and a small handheld device up to a computer. The computer system **900** includes one or more processors **902**, and further can include an electronic display device **904**, a main memory **906** (e.g., random access memory (RAM)), storage device **908** (e.g., hard disk drive), removable storage device **910** (e.g., optical disk drive), user interface devices **912** (e.g., keyboards, touch screens, keypads, mice or other pointing devices, etc.), and a communication interface **914** (e.g., wireless network interface). The communication interface **914** allows software and data to be transferred between the computer system **900** and external devices via a link. The system may also include a communications infrastructure **916** (e.g., a communications bus, cross-over bar, or network) to which the aforementioned devices/modules are connected.

Information transferred via communications interface **914** may be in the form of signals such as electronic, electromagnetic, optical, or other signals capable of being received by communications interface **914**, via a communication link that carries signals and may be implemented using wire or cable, fiber optics, a phone line, a cellular phone link, a radio frequency link, and/or other communication channels. With such a communications interface, it is contemplated that the one or more processors **902** might receive information from a network, or might output information to the network in the course of performing the above-described method steps. Furthermore, method embodiments of the present invention may execute solely upon the processors or may execute over a network, such as the Internet, in conjunction with remote processors that shares a portion of the processing.

The term “non-transient computer readable medium” is used generally to refer to media such as main memory, secondary memory, removable storage, and storage devices, such as hard disks, flash memory, disk drive memory, CD-ROM and other forms of persistent memory and shall not be construed to cover transitory subject matter, such as carrier waves or signals. Examples of computer code include machine code, such as produced by a compiler, and files containing higher level code that are executed by a computer using an interpreter. Computer readable media may also be computer code transmitted by a computer data signal embodied in a carrier wave and representing a sequence of instructions that are executable by a processor.

In an example, a patient may be placed on patient transport table **808** of the MRI system **800**. The controller **812** causes the magnet system **804** to provide a DESS sequence for a volume of the patient (step **704**). In this example, the volume is a knee of the patient. Signals S_{1 }and S_{2 }are acquired by the MRI system **800** (step **708**). The signals S_{1 }and S_{2 }are used to provide a T_{2 }map for a plurality of slices of the knee by determining repetition time (TR), echo time (TE), flip angle α, longitudinal relaxation time T_{1}, and where the DESS scan has a spoiler gradient with an amplitude G and a duration τ and ignoring echo pathways having spent more than two repetition times in the transverse plane (step **712**).

In this embodiment, S_{1 }and S_{2 }are used to provide a T_{2 }map using a function

where ƒ(α, TR, T1) is a function that is not proportional to

More preferably, in this embodiment

It should be noted that the equation used in this embodiment, is the same as Eq. (7), when solving for T_{2}. Therefore, using Eq. (7), in the specification and claims would be the same as using the equation in this embodiment. As mentioned above, Eq. (7) may be used to provide the T_{2 }map from signals S_{1 }and S_{2 }with known values of TR, TE, α, and an estimate of the relaxation time (T_{1}). The use of Eq. (7) allows echo pathways that have spent more than two repetition times in the transverse plane to be ignored. In addition, the use of Eq. (7) allows the T_{2 }map to be generated, while ignoring diffusivity, and estimiting T_{1}.

In this example, the controller **812** may be used to generate and then display an image on the display **904** (step **716**). In this example, a plurality of T_{2 }map images are displayed, where each T_{2 }image is of a slice of the volume, so that the plurality of T_{2 }map images from a plurality of slices of the knee to provide a 3D view of the knee.

MRI systems signals measure magnetization that is perpendicular to the main magnetic field. Perpendicular signals are said to be in the transverse plane. The signals measured in steady-state sequences such as DESS are composed of magnetization components that have evolved over many repetition times (TRs). During some TRs, the magnetization is parallel to the main magnetic field, and during others, it is perpendicular to the field (in the transverse plane). In the specification and claims, ignoring echo pathways with more than two repetition times in the transverse plane means that it is assumed that the measured signal does not have magnetization components that have spent more than two repetition times in the transverse plane.

While this invention has been described in terms of several preferred embodiments, there are alterations, permutations, modifications and various substitute equivalents, which fall within the scope of this invention. It should also be noted that there are many alternative ways of implementing the methods and apparatuses of the present invention. It is therefore intended that the following appended claims be interpreted as including all such alterations, permutations, modifications, and various substitute equivalents as fall within the true spirit and scope of the present invention.

## Claims

1. A method for providing an estimated 3D T2 map for magnetic resonance imaging using a Double-Echo Steady-State (DESS) sequence for a volume of an object in a magnetic resonance imaging (MRI) system, comprising: T 2 = - 2 ( TR - TE ) log [ ( S 2 S 1 sin 2 α 2 ) f ( α, TR, T 1 ) ], wherein f(α, TR, T1) is a function that is not proportional to sin 2 α 2 and TR is a repetition time, TE is an echo time, and α is a flip angle; and

- providing a DESS scan of the volume by the MRI system, wherein the DESS scan has a spoiler gradient with an amplitude G and a duration τ;

- acquiring signals S1 and S2 by the MRI system; and

- providing a T2 map for a plurality of slices of the volume based on signals S1 and S2, the step of providing the T2 map further comprising determining repetition time (TR), echo time (TE), flip angle α, and an estimate of the longitudinal relaxation time (T1), and ignoring echo pathways having spent more than two repetition times in the transverse plane, wherein the step of providing a T2 map determines T2 using a function

- displaying the T2 map.

2. The method, as recited in claim 1, wherein f ( α, TR, T 1 ) = ( 1 - ( cos α ) e - TR T 1 ) ( 1 + e - TR T 1 ).

3. A method for providing an estimated 3D T2 map for magnetic resonance imaging using a Double-Echo Steady-State (DESS) sequence for a volume of an object in a magnetic resonance imaging (MRI) system, comprising: T 2 = - 2 ( TR - TE ) log [ ( S 2 S 1 sin 2 α 2 ) f ( α, TR, T 1 ) ], wherein f(α, TR, T1) is a function that is not proportional to sin 2 α 2 and TR is a repetition time, TE is an echo time, and a is a flip angle; and

- providing a DESS scan of the volume by the MRI system;

- acquiring signals S1 and S2 by the MRI system;

- providing a T2 map for a plurality of slices of the volume based on signals S1 and S2, using the equation

- displaying the T2 map.

4. The method, as recited in claim 3, wherein f ( α, TR, T 1 ) = ( 1 - ( cos α ) e - TR T 1 ) ( 1 + e - TR T 1 ).

**Referenced Cited**

**U.S. Patent Documents**

4746865 | May 24, 1988 | Kasugai |

8508225 | August 13, 2013 | Granlund et al. |

8706188 | April 22, 2014 | Koo |

9915750 | March 13, 2018 | Hurlimann |

20120112743 | May 10, 2012 | Granlund |

**Other references**

- Sviensson, Bragi “A Simple Analytic Method for Estimating T2 in the Knee from DESS” Magnetic Resonance Imaging, vol. 38 p. 63-70, Dec. 22, 2016.

**Patent History**

**Patent number**: 10775463

**Type:**Grant

**Filed**: Apr 7, 2017

**Date of Patent**: Sep 15, 2020

**Patent Publication Number**: 20170299679

**Assignee**: The Board of Trustees of the Leland Stanford Junior University (Palo Alto, CA)

**Inventors**: Brian A. Hargreaves (Menlo Park, CA), Bragi Sveinsson (Stanford, CA)

**Primary Examiner**: Tung X Nguyen

**Assistant Examiner**: Robert P Alejnikov, Jr.

**Application Number**: 15/482,351

**Classifications**

**Current U.S. Class**:

**Using A Nuclear Resonance Spectrometer System (324/307)**

**International Classification**: G01R 33/50 (20060101); G01R 33/483 (20060101); G01R 33/48 (20060101);